We study the problem of the essential self-adjointness of Laplacians on Riemannian manifolds. We show that a sufficient condition is if the boundary of a manifold M. by which we mean M̄\M, where M̄ is the metric completion of M, is almost polar set. Two other results concern special cases, when the boundary is some sort of fractal set or even a manifold. It is shown that the boundary is almost polar set in the cases under certain dimensional restrictions.
- Essential self-adjointness